Diamond 4C

I. Cut (車工)

鑽石切工締造璀璨光芒

高折射率造就了鑽石的璀璨光芒,使其聞名於世。許多人會把鑽石切工等同於鑽石的形狀(圓形、心形、橢圓形、馬眼形、梨形)。實際上鑽石切工等級取決於其刻面與光線的相互作用結果。

II. Clarity (淨度)

鑽石淨度是指其無內含物和表面特徵的程度

天然鑽石是碳元素在高溫高壓的環境下形成的。而這一過程,也導致了每顆鑽石有內部的特徵,稱為“內含物”,在鑽石表面的特徵則稱為“表面特徵”。

對鑽石淨度的評定,包括了對上述特徵的數量、大小、可見度、類型、位置和對鑽石整體外觀的影響程度的鑑定。儘管世上沒有絕對完美無瑕的天然鑽石,但淨度越高的鑽石,價值越高。

GIA 的鑽石淨度標準分為 6 個類別,11 個等級。

III. Carat (克拉重量)

鑽石克拉重量用於衡量鑽石的外觀尺寸

克拉是用於衡量鑽石重量的單位。1 克拉等於 200 毫克。

在對鑽石重量進行測量時,1 克拉又等同於 100 “分”,從而使克拉重量精確到小數點後兩位。珠寶商可以直接用“分” 來描述一顆重量小於1 克拉的鑽石。比如,0.25 克拉的鑽石又被稱作“二十五分”。但對於1 克拉以上的鑽石, 只能用精確到百分位的“克拉”來描述。比如,1.08 克拉的鑽石只能用“一點零八克拉” 來說明其重量。

在所有其他條件都一樣的情況下,鑽石越大,其稀有程度就越高,也越受青睞。因此,鑽石的價格會隨著鑽石克拉重量的增加而上升。

IV. Color (顏色)

鑽石顏色實際上是指其無色的程度

對大多數寶石級鑽石來說,其顏色鑑定標準取決於它的無色程度。一顆不含化學雜質且結構完美的鑽石就像純淨的水滴一樣,是沒有色彩的,且具有更高的價值。GIA 創立了D 到Z 鑽石顏色分級系統,通過在精確受控的照明、觀測條件下,將鑽石與比色石比對,來鑑定其無色程度。

Codebook

names(diamonds)
 [1] "carat"     "cut"       "color"     "clarity"   "depth"     "table"    
 [7] "price"     "x"         "y"         "z"         "price_grp"
vars= names(diamonds)
codebook= summary(diamonds) %>% split(col(.))
names(codebook)= vars
descript= 
  c('克拉','裁切等級','鑽石顏色','鑽石淨度', '總深度百分比','鑽石的最大刻面', 
    '價錢(美元)','長度(mm)', '寬度(mm)','深度(mm)')
cb = rbind.data.frame(descript, codebook) %>% t
kable(cb) %>% kable_classic(html_font = 'Times New Roman')
carat 克拉 Min. :0.2000 1st Qu.:0.4000 Median :0.7000 Mean :0.7979 3rd Qu.:1.0400 Max. :5.0100
cut 裁切等級 Fair : 1610 Good : 4906 Very Good:12082 Premium :13791 Ideal :21551
color 鑽石顏色 D: 6775 E: 9797 F: 9542 G:11292 H: 8304 I: 5422 J: 2808
clarity 鑽石淨度 SI1 :13065 VS2 :12258 SI2 : 9194 VS1 : 8171 VVS2 : 5066 VVS1 : 3655 (Other): 2531
depth 總深度百分比 Min. :43.00 1st Qu.:61.00 Median :61.80 Mean :61.75 3rd Qu.:62.50 Max. :79.00
table 鑽石的最大刻面 Min. :43.00 1st Qu.:56.00 Median :57.00 Mean :57.46 3rd Qu.:59.00 Max. :95.00
price 價錢(美元) Min. : 326 1st Qu.: 950 Median : 2401 Mean : 3933 3rd Qu.: 5324 Max. :18823
x 長度(mm) Min. : 0.000 1st Qu.: 4.710 Median : 5.700 Mean : 5.731 3rd Qu.: 6.540 Max. :10.740
y 寬度(mm) Min. : 0.000 1st Qu.: 4.720 Median : 5.710 Mean : 5.735 3rd Qu.: 6.540 Max. :58.900
z 深度(mm) Min. : 0.000 1st Qu.: 2.910 Median : 3.530 Mean : 3.539 3rd Qu.: 4.040 Max. :31.800
price_grp 克拉 min-Q1 :13490 Q1-median:13495 median-Q3:13470 Q3-Max :13485

Distribution

Cut

diamonds %>%
  ggplot(aes(x=cut,y=price, fill=cut)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)

Clarity

diamonds %>%
  ggplot(aes(x=clarity,y=price, fill=clarity)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)

Carat

diamonds$carat_grp= cut(diamonds$carat, fivenum(diamonds$carat),include.lowest = T)
Found more than one class "tbl_df" in cache; using the first, from namespace 'tibble'
Also defined by ‘memisc’
diamonds %>%
  ggplot(aes(x=carat_grp,y=price, fill=carat_grp)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)

Color

diamonds %>%
  ggplot(aes(x=color,y=price, fill=color)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)

Correlation matrix

M= 
  diamonds %>% 
  dplyr::select(price, carat,depth,table,x,y,z) %>% 
  cor
  
M[lower.tri(M)] <- NA
M %>% pheatmap(display_numbers = T, number_color = 'white', cluster_rows=F, cluster_cols=F, na_col="white", color = rev(brewer.pal(10, 'RdBu')))

Scatter plot

diamonds %>%
  ggplot(aes(carat, price, col= color))+
  geom_point() + facet_grid(cut~clarity)

Summary table

diamonds$price_grp= 
  cut(diamonds$price, fivenum(diamonds$price), include.lowest = T, labels = c('<Q1','Q1-median','median-Q3', '>Q3'))
Found more than one class "tbl_df" in cache; using the first, from namespace 'tibble'
Also defined by ‘memisc’
library(moonBook)
mytable(price_grp~.,diamonds) %>% mytable2df() %>% kable() %>% kable_classic()
name <Q1 Q1-median median-Q3 >Q3 p
(N=13490) (N=13495) (N=13470) (N=13485)
carat 0.3 ± 0.0 0.5 ± 0.1 0.9 ± 0.2 1.4 ± 0.4 0.000
cut 0.000
- Fair 88 ( 0.7%) 462 ( 3.4%) 667 ( 5.0%) 393 ( 2.9%)
- Good 1057 ( 7.8%) 1087 ( 8.1%) 1634 (12.1%) 1128 ( 8.4%)
- Very Good 3129 (23.2%) 2533 (18.8%) 3369 (25.0%) 3051 (22.6%)
- Premium 2907 (21.5%) 3069 (22.7%) 3504 (26.0%) 4311 (32.0%)
- Ideal 6309 (46.8%) 6344 (47.0%) 4296 (31.9%) 4602 (34.1%)
color 0.000
- D 1878 (13.9%) 2047 (15.2%) 1698 (12.6%) 1152 ( 8.5%)
- E 2790 (20.7%) 2984 (22.1%) 2471 (18.3%) 1552 (11.5%)
- F 2268 (16.8%) 2642 (19.6%) 2520 (18.7%) 2112 (15.7%)
- G 2917 (21.6%) 2962 (21.9%) 2227 (16.5%) 3186 (23.6%)
- H 2023 (15.0%) 1448 (10.7%) 2308 (17.1%) 2525 (18.7%)
- I 1184 ( 8.8%) 888 ( 6.6%) 1459 (10.8%) 1891 (14.0%)
- J 430 ( 3.2%) 524 ( 3.9%) 787 ( 5.8%) 1067 ( 7.9%)
clarity 0.000
- I1 55 ( 0.4%) 189 ( 1.4%) 319 ( 2.4%) 178 ( 1.3%)
- SI2 1024 ( 7.6%) 1530 (11.3%) 4104 (30.5%) 2536 (18.8%)
- SI1 2933 (21.7%) 2859 (21.2%) 4119 (30.6%) 3154 (23.4%)
- VS2 3389 (25.1%) 3109 (23.0%) 2200 (16.3%) 3560 (26.4%)
- VS1 2297 (17.0%) 2189 (16.2%) 1433 (10.6%) 2252 (16.7%)
- VVS2 1784 (13.2%) 1530 (11.3%) 666 ( 4.9%) 1086 ( 8.1%)
- VVS1 1392 (10.3%) 1356 (10.0%) 458 ( 3.4%) 449 ( 3.3%)
- IF 616 ( 4.6%) 733 ( 5.4%) 171 ( 1.3%) 270 ( 2.0%)
depth 61.8 ± 1.2 61.7 ± 1.4 61.8 ± 1.7 61.7 ± 1.5 0.000
table 57.0 ± 2.1 57.2 ± 2.3 57.9 ± 2.3 57.8 ± 2.1 0.000
price 687.9 ± 149.4 1563.3 ± 443.6 3790.7 ± 852.7 9692.1 ± 3657.3 0.000
x 4.4 ± 0.2 5.2 ± 0.4 6.2 ± 0.4 7.2 ± 0.6 0.000
z 2.7 ± 0.1 3.2 ± 0.4 3.8 ± 0.3 4.4 ± 0.4 0.000
carat_grp 0.000
- [0.2,0.4] 12076 (89.5%) 2315 (17.2%) 0 ( 0.0%) 0 ( 0.0%)
- (0.4,0.7] 1413 (10.5%) 9776 (72.4%) 1573 (11.7%) 9 ( 0.1%)
- (0.7,1.04] 1 ( 0.0%) 1386 (10.3%) 9434 (70.0%) 2578 (19.1%)
- (1.04,5.01] 0 ( 0.0%) 18 ( 0.1%) 2463 (18.3%) 10898 (80.8%)

Building the Linear Model

diamonds1 = diamonds
diamonds1$cut <- factor(diamonds1$cut, ordered=F)
diamonds1$color <- factor(diamonds1$color, ordered=F)
diamonds1$clarity <- factor(diamonds1$clarity, ordered=F)
m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamonds1)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)

mt = memisc::mtable(m1, m2, m3, m4, m5, sdigits=4, getSummary=NULL,  
               summary.stats=c("R-squared", "adj. R-squared", "sigma", "F","p",
                               "Log-likelihood", "Deviance", "AIC", "BIC", "N"))
m1 m2 m3 m4 m5
(Intercept) 2 . 821*** 1 . 039*** 0 . 685*** 0 . 891*** −0 . 172***
(0 . 006) (0 . 019) (0 . 020) (0 . 018) (0 . 011)
I(carat^(1/3)) 5 . 558*** 8 . 568*** 8 . 703*** 8 . 438*** 9 . 144***
(0 . 007) (0 . 032) (0 . 031) (0 . 028) (0 . 016)
carat −1 . 137*** −1 . 163*** −0 . 992*** −1 . 093***
(0 . 012) (0 . 011) (0 . 010) (0 . 006)
cut: Good/Fair 0 . 159*** 0 . 158*** 0 . 077***
(0 . 007) (0 . 006) (0 . 004)
cut: Very Good/Fair 0 . 236*** 0 . 235*** 0 . 112***
(0 . 007) (0 . 006) (0 . 003)
cut: Premium/Fair 0 . 236*** 0 . 235*** 0 . 135***
(0 . 007) (0 . 006) (0 . 003)
cut: Ideal/Fair 0 . 316*** 0 . 316*** 0 . 160***
(0 . 007) (0 . 006) (0 . 003)
color: E/D −0 . 026*** −0 . 055***
(0 . 004) (0 . 002)
color: F/D −0 . 036*** −0 . 096***
(0 . 004) (0 . 002)
color: G/D −0 . 063*** −0 . 163***
(0 . 003) (0 . 002)
color: H/D −0 . 196*** −0 . 256***
(0 . 004) (0 . 002)
color: I/D −0 . 295*** −0 . 375***
(0 . 004) (0 . 002)
color: J/D −0 . 426*** −0 . 511***
(0 . 005) (0 . 003)
clarity: SI2 0 . 420***
(0 . 005)
clarity: SI1 0 . 585***
(0 . 005)
clarity: VS2 0 . 733***
(0 . 005)
clarity: VS1 0 . 803***
(0 . 005)
clarity: VVS2 0 . 934***
(0 . 005)
clarity: VVS1 1 . 006***
(0 . 005)
clarity: IF 1 . 101***
(0 . 006)
R-squared 0 . 9236 0 . 9349 0 . 9391 0 . 9514 0 . 9839
adj. R-squared 0 . 9236 0 . 9349 0 . 9391 0 . 9514 0 . 9839
sigma 0 . 2805 0 . 2588 0 . 2504 0 . 2237 0 . 1286
F 652012 . 0628 387489 . 3661 138654 . 5235 87959 . 4667 173791 . 0840
p 0 . 0000 0 . 0000 0 . 0000 0 . 0000 0 . 0000
Log-likelihood −7962 . 4993 −3631 . 3185 −1837 . 4158 4235 . 2405 34091 . 2720
Deviance 4242 . 8307 3613 . 3602 3380 . 8373 2699 . 2124 892 . 2143
AIC 15930 . 9985 7270 . 6370 3690 . 8316 −8442 . 4809 −68140 . 5440
BIC 15957 . 6854 7306 . 2195 3761 . 9966 −8317 . 9421 −67953 . 7358
N 53940 53940 53940 53940 53940

Significance: *** = p < 0.001; ** = p < 0.01; * = p < 0.05

---
title: " with R Markdown"
author: "Jimmy Cheng"
date: "`r Sys.Date()`"
output:
  html_notebook:
    toc: yes
    toc_float: true
    #citation_package: biblatex
#bibliography: references.bib
#csl: bmj.csl
---

```{r setup, include=F}
knitr::opts_chunk$set(
	fig.height = 6,
	fig.width = 9,
	dev = "svg",
	dpi = 600
)
#devtools::install_github("gadenbuie/xaringanExtra")
xaringanExtra::use_panelset()
options(knitr.kable.NA = '')

library(tidyverse)
library(knitr)
library(kableExtra)
library(RColorBrewer)
library(pheatmap)
```

![](images/4cs.jpg)

# **Diamond 4C**

## **I. Cut (車工)**

> #### 鑽石切工締造璀璨光芒

高折射率造就了鑽石的璀璨光芒，使其聞名於世。許多人會把鑽石切工等同於鑽石的形狀（圓形、心形、橢圓形、馬眼形、梨形）。實際上鑽石切工等級取決於其刻面與光線的相互作用結果。

![](https://mrsring.co/wp-content/uploads/20191112183537_97.jpg)

## **II. Clarity (淨度)**

> #### 鑽石淨度是指其無內含物和表面特徵的程度

天然鑽石是碳元素在高溫高壓的環境下形成的。而這一過程，也導致了每顆鑽石有內部的特徵，稱為"內含物"，在鑽石表面的特徵則稱為"表面特徵"。

對鑽石淨度的評定，包括了對上述特徵的數量、大小、可見度、類型、位置和對鑽石整體外觀的影響程度的鑑定。儘管世上沒有絕對完美無瑕的天然鑽石，但淨度越高的鑽石，價值越高。

GIA 的鑽石淨度標準分為 6 個類別，11 個等級。

![](http://media.valigara.com/cl/172/user_images/Clarity.jpg)

## **III. Carat (克拉重量)**

> #### 鑽石克拉重量用於衡量鑽石的外觀尺寸

克拉是用於衡量鑽石重量的單位。1 克拉等於 200 毫克。

在對鑽石重量進行測量時，1 克拉又等同於 100 "分"，從而使克拉重量精確到小數點後兩位。珠寶商可以直接用"分" 來描述一顆重量小於1 克拉的鑽石。比如，0.25 克拉的鑽石又被稱作"二十五分"。但對於1 克拉以上的鑽石， 只能用精確到百分位的"克拉"來描述。比如，1.08 克拉的鑽石只能用"一點零八克拉" 來說明其重量。

在所有其他條件都一樣的情況下，鑽石越大，其稀有程度就越高，也越受青睞。因此，鑽石的價格會隨著鑽石克拉重量的增加而上升。

![](http://media.valigara.com/cl/172/user_images/caratsizes.jpg){width="900"}

## **IV. Color (顏色)**

> #### 鑽石顏色實際上是指其無色的程度

對大多數寶石級鑽石來說，其顏色鑑定標準取決於它的無色程度。一顆不含化學雜質且結構完美的鑽石就像純淨的水滴一樣，是沒有色彩的，且具有更高的價值。GIA 創立了D 到Z 鑽石顏色分級系統，通過在精確受控的照明、觀測條件下，將鑽石與比色石比對，來鑑定其無色程度。 ![](http://media.valigara.com/cl/172/user_images/GIA-Color-Grading-Scale-1.jpg){width="900"}

## **Codebook**

```{r}
names(diamonds)
vars= names(diamonds)
codebook= summary(diamonds) %>% split(col(.))
names(codebook)= vars
descript= 
  c('克拉','裁切等級','鑽石顏色','鑽石淨度', '總深度百分比','鑽石的最大刻面', 
    '價錢(美元)','長度(mm)', '寬度(mm)','深度(mm)')
cb = rbind.data.frame(descript, codebook) %>% t
kable(cb) %>% kable_classic(html_font = 'Times New Roman')
```

![](images/Anatomy_Graphic_Large.jfif)

## **Distribution** {.panelset}

### Cut

```{r}
diamonds %>%
  ggplot(aes(x=cut,y=price, fill=cut)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)
```

### Clarity

```{r}
diamonds %>%
  ggplot(aes(x=clarity,y=price, fill=clarity)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)
```

### Carat

```{r}
diamonds$carat_grp= cut(diamonds$carat, fivenum(diamonds$carat),include.lowest = T)

diamonds %>%
  ggplot(aes(x=carat_grp,y=price, fill=carat_grp)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)
```

### Color

```{r}
diamonds %>%
  ggplot(aes(x=color,y=price, fill=color)) +
  geom_violin()->p; plotly::ggplotly(p,width = 9)
```

## **Correlation matrix**

```{r}
M= 
  diamonds %>% 
  dplyr::select(price, carat,depth,table,x,y,z) %>% 
  cor
  
M[lower.tri(M)] <- NA
M %>% pheatmap(display_numbers = T, number_color = 'white', cluster_rows=F, cluster_cols=F, na_col="white", color = rev(brewer.pal(10, 'RdBu')))

```

## **Scatter plot**

```{r}
diamonds %>%
  ggplot(aes(carat, price, col= color))+
  geom_point() + facet_grid(cut~clarity)
```

## **Summary table**
```{r}
diamonds$price_grp= 
  cut(diamonds$price, fivenum(diamonds$price), include.lowest = T, labels = c('<Q1','Q1-median','median-Q3', '>Q3'))

library(moonBook)
mytable(price_grp~.,diamonds) %>% mytable2df() %>% kable() %>% kable_classic()
```



## **Building the Linear Model**
```{r results='hide'}
diamonds1 = diamonds
diamonds1$cut = factor(diamonds1$cut, ordered=F)
diamonds1$color = factor(diamonds1$color, ordered=F)
diamonds1$clarity = factor(diamonds1$clarity, ordered=F)

m1 <- lm(I(log(price)) ~ I(carat^(1/3)), data = diamonds1)
m2 <- update(m1, ~ . + carat)
m3 <- update(m2, ~ . + cut)
m4 <- update(m3, ~ . + color)
m5 <- update(m4, ~ . + clarity)

mt = memisc::mtable(m1, m2, m3, m4, m5, sdigits=4, getSummary=NULL,  
               summary.stats=c("R-squared", "adj. R-squared", "sigma", "F","p",
                               "Log-likelihood", "Deviance", "AIC", "BIC", "N"))

```

```{r}
knit_print.mtable <- function(x) knitr::asis_output(memisc::format_html(x))
knit_print.mtable(mt)
```


## **Rerence**

1.  <https://www.bluenile.com/tw/education/diamonds/cut>
2.  <https://4cs.gia.edu/en-us/diamond-color/>
3.  <https://www.directdiam.com/pages/diamonds-4cs>
4.  <https://gallery.azure.ai/Experiment/Diamond-dataset>
5.  panelset: <https://pkg.garrickadenbuie.com/xaringanExtra/panelset/rmarkdown.html?panelset1=tab-a&panelset=tabset%252Fpanelset>
6.  <https://rstudio-pubs-static.s3.amazonaws.com/211979_60432c2480574f419f646c9834768a77.html>
